Ga2O3-based crystal film, and crystal multilayer structure

ABSTRACT

A method of growing a conductive Ga 2 O 3 -based crystal film by MBE includes producing a Ga vapor and a Si-containing vapor and supplying the vapors as molecular beams onto a surface of a Ga 2 O 3 -based crystal substrate so as to grow the Ga 2 O 3 -based crystal film. The Ga 2 O 3 -based crystal film includes a Si-containing Ga 2 O 3 -based single crystal film. The Si-containing vapor is produced by heating Si or a Si compound and Ga while allowing the Si or a Si compound to contact with the Ga.

The present application is based on Japanese patent application No. 2016-111972 filed on Jun. 3, 2016, the entire contents of which are incorporated herein by reference.

BACKGROUND OF THE INVENTION 1. Field of the Invention

The invention relates to a method of growing a Ga₂O₃-based crystal film and a crystal multilayer structure grown by the method.

2. Description of the Related Art

A method of growing a Ga₂O₃-based crystal film is known which uses MBE and Sn as a dopant (see e.g. WO2013/080972).

WO2013/080972 states that if Si is used as a dopant, it is difficult to control the vapor pressure of vaporized Si source such as Si, SiO and SiO₂ to control the Si concentration of the Ga₂O₃-based crystal film. Also it states that, therefore, Sn is used as the dopant instead of using Si so as to control the carrier concentration of the Ga₂O₃-based crystal film with high accuracy.

SUMMARY OF THE INVENTION

When Sn is used as the dopant for the Ga₂O₃-based crystal film, a problem may arise that Sn is difficult to introduce into the film (i.e., doping delayed) at the initial growth stage of the Ga₂O₃-based crystal film and is likely to segregate on the growth surface.

It is an object of the invention to provide a method of growing by MBE a Ga₂O₃-based crystal film that allows the highly accurate control of a dopant concentration so as to enhance the uniformity of dopant concentration distribution, as well as a crystal multilayer structure grown by the method.

According to an embodiment of the invention, a method of growing a Ga₂O₃-based crystal film by MBE defined by [1] to [4] below is provided.

[1] A method of growing a conductive Ga₂O₃-based crystal film by MBE, comprising producing a Ga vapor and a Si-containing vapor and supplying the vapors as molecular beams onto a surface of a Ga₂O₃-based crystal substrate so as to grow the Ga₂O₃-based crystal film,

wherein the Ga₂O₃-based crystal film comprises a Si-containing Ga₂O₃-based single crystal film, and

wherein the Si-containing vapor is produced by heating Si or a Si compound and Ga while allowing the Si or the Si compound to contact with the Ga.

[2] The method according to [1], wherein the Si compound is provided as a cell of an MBE apparatus comprising SiO₂, and

wherein the Si-containing vapor is produced by heating the cell and the Ga enclosed by the cell while allowing the cell to contact with the Ga.

[3] The method according to [1], wherein the Si-containing vapor is produced by heating a cell of an MBE apparatus and the Si or the Si compound and the Ga which are enclosed by the cell while allowing the Si or the Si compound to contact with the Ga.

[4] The method according to [3], wherein the Si compound comprises one of SiO and SiO₂.

According to another embodiment of the invention, a crystal multilayer structure defined by [5] below is provided.

[5] A crystal multilayer structure, comprising:

a Ga₂O₃-based crystal substrate;

an undoped Ga₂O₃-based crystal film grown on the Ga₂O₃-based crystal substrate;

a first undoped (AlGa)₂O₃ crystal film grown directly on the undoped Ga₂O₃-based crystal film;

a Si-doped (AlGa)₂O₃ crystal film grown directly on the first undoped (AlGa)₂O₃ crystal film, the Si-doped (AlGa)₂O₃ crystal film having a thickness of not more than 10 nm and comprising Si at a concentration of not less than 3.0×10¹⁷/cm³ and not more than 3.5×10¹⁹/cm³; and

a second undoped (AlGa)₂O₃ crystal film grown directly on the (AlGa)₂O₃ crystal film.

Effects of the Invention

According to an embodiment of the invention, a method of growing by MBE a Ga₂O₃-based crystal film can be provided that allows the highly accurate control of a dopant concentration so as to enhance the uniformity of dopant concentration distribution, as well as a crystal multilayer structure grown by the method.

BRIEF DESCRIPTION OF THE DRAWINGS

Next, the present invention will be explained in more detail in conjunction with appended drawings, wherein:

FIG. 1 is a vertical cross sectional view showing a Ga₂O₃-based crystal substrate and a Ga₂O₃-based crystal film in a first embodiment;

FIG. 2 is a diagram illustrating an exemplary configuration of an MBE apparatus used for growing the Ga₂O₃-based crystal film;

FIG. 3 is a vertical cross sectional view showing a crystal multilayer structure in a third embodiment;

FIG. 4 is a vertical cross sectional view showing a specific example of the crystal multilayer structure in the third embodiment;

FIG. 5A is a diagram illustrating a concentration distribution of Si added as a dopant in a thickness direction of the Ga₂O₃-based crystal film and the Ga₂O₃-based crystal substrate;

FIG. 5B is a diagram illustrating a concentration distribution of Sn added as a dopant in a thickness direction of the Ga₂O₃-based crystal film and the Ga₂O₃-based crystal substrate; and

FIG. 6 is a diagram illustrating a relation between an effective donor concentration N_(d)-N_(a) in the Ga₂O₃ crystal film and temperature of a second cell which is formed of SiO₂ and contains Ga powder.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS First Embodiment

Ga₂O₃-Based Crystal Film

FIG. 1 is a vertical cross sectional view showing a Ga₂O₃-based crystal substrate and a Ga₂O₃-based crystal film in the first embodiment.

A Ga₂O₃-based crystal film 1 is formed by epitaxially growing a Ga₂O₃-based single crystal on a Ga₂O₃-based crystal substrate 2 by MBE. MBE is a crystal growth method in which raw materials as pure element or compound are heated in evaporators called cells and vapors generated by heat are supplied in the form of molecular beams onto the surface of the substrate to epitaxially grow a crystal.

The Ga₂O₃-based crystal film 1 is formed of an n-type β-Ga₂O₃-based single crystal containing Si as a dopant. The Ga₂O₃-based single crystal here is a Ga₂O₃ single crystal, or a Ga₂O₃ single crystal doped with an element such as Al and In, and may be, e.g., a (Ga_(x)Al_(y)In_((1-x-y)))₂O₃ (0<x≤1, 0≤y<1, 0<x+y≤1) single crystal which is a Ga₂O₃ single crystal doped with Al and In. The band gap is widened by adding Al and is narrowed by adding In.

The Ga₂O₃-based crystal substrate 2 is formed of a β-Ga₂O₃-based single crystal and may contain various dopants according to the type of device for which the Ga₂O₃-based crystal film 1 and the Ga₂O₃-based crystal substrate 2 are used. For example, Mg, etc., may be added as a dopant to increase resistance of the Ga₂O₃-based crystal substrate 2 when the Ga₂O₃-based crystal film 1 and the Ga₂O₃-based crystal substrate 2 are used in a lateral semiconductor device, and Si or Sn, etc., may be added as a dopant to decrease resistance of the Ga₂O₃-based crystal substrate 2 when the Ga₂O₃-based crystal film 1 and the Ga₂O₃-based crystal substrate 2 are used in a vertical semiconductor device.

The Ga₂O₃-based crystal substrate 2 is cut out from, e.g., a doped β-Ga₂O₃ single crystal ingot made by the EFG method. The β-Ga₂O₃ single crystal ingot may alternatively be made by the FZ method. The obtained ingot is sliced to a thickness of, e.g., about 1 mm so that the principal surface has a desired plane orientation, thereby formed into a substrate. Then, a grinding and polishing process is performed to a thickness of about 300 to 600 μm.

Method of Manufacturing Ga₂O₃-Based Crystal Film

FIG. 2 shows an exemplary configuration of an MBE apparatus used for growing the Ga₂O₃-based crystal film. An MBE apparatus 3 is provided with a vacuum chamber 10, a substrate holder 11 supported in the vacuum chamber 10 and provided to hold the Ga₂O₃-based crystal substrate 2, a heating device 12 held on the substrate holder 11 and provided to heat the Ga₂O₃-based crystal substrate 2, plural cells 13 (13 a, 13 b, 13 c) filled with source atoms constituting the Ga₂O₃-based crystal film 1, heaters 14 (14 a, 14 b, 14 c) for hearing the cells 13, a gas supply pipe 15 for supplying oxygen-based gas into the vacuum chamber 10, and a vacuum pump 16 for exhausting the air from the vacuum chamber 10. It is configured that the substrate holder 11 can be rotated by a motor (not shown) via a shaft 110.

The first cell 13 a contains Ga as a Ga source for the Ga₂O₃-based crystal film 1. The form of Ga contained in the first cell 13 a is not specifically limited and is typically a solid such as powder or particles. The first cell 13 a is formed of, e.g., PBN (Pyrolytic Boron Nitride).

The second cell 13 b is formed of SiO₂ and is used as a source of Si added to the Ga₂O₃-based crystal film 1. The second cell 13 b contains Ga. The form of Ga contained in the second cell 13 b is not specifically limited and is typically a solid such as powder or particles. Generally, the amount of Ga in the second cell 13 b is about half the maximum capacity of the second cell 13 b.

The third cell 13 c contains a material other than Ga and Si, e.g., contains an Al source when the Ga₂O₃-based crystal film 1 is formed of a β-(Al_(x)Ga_(1-x))₂O₃ single crystal. It is not necessary to provide the third cell 13 c when the Ga₂O₃-based crystal film 1 is formed of a β-Ga₂O₃ single crystal.

A shutter is provided at an opening of each of the first cell 13 a, the second cell 13 b and the third cell 13 c.

Firstly, the preliminarily-formed Ga₂O₃-based crystal substrate 2 is attached to the substrate holder 11 of the MBE apparatus 3. Next, the vacuum pump 16 is activated to reduce atmospheric pressure in the vacuum chamber 10 to about 1×10⁻⁸ Pa. Then, the Ga₂O₃-based crystal substrate 2 is heated by the heating device 12. Here, radiation heat from heat source such as graphite heater of the heating device 12 is thermally transferred to the Ga₂O₃-based crystal substrate 2 via the substrate holder 11 and the Ga₂O₃-based crystal substrate 2 is thereby heated.

After the Ga₂O₃-based crystal substrate 2 is heated to a predetermined temperature, an oxygen-based gas such as ozone gas or oxygen radical is supplied into the vacuum chamber 10 through the gas supply pipe 15. Partial pressure of the oxygen-based gas is, e.g., 5×10⁻⁴ Pa.

After a period of time required for stabilization of gas pressure in the vacuum chamber 10 (e.g., after 5 minutes), the first cell 13 a, the second cell 13 b and, if necessary, the third cell 13 c are heated by the heaters 14 while rotating the substrate holder 11 so that vapors containing raw materials of the Ga₂O₃-based crystal film 1 are produced and are radiated as molecular beams onto the surface of the Ga₂O₃-based crystal substrate 2. Accordingly, a β-Ga₂O₃-based single crystal is epitaxially grown on the Ga₂O₃-based crystal substrate 2 while being doped with Si, and the Ga₂O₃-based crystal film 1 is thereby formed.

The first cell 13 a is heated to, e.g., 900° C. so that Ga contained in the first cell 13 a produces a Ga vapor. The beam-equivalent pressure (BEP) of the Ga vapor is 2×10⁻⁴ Pa.

The second cell 13 b is heated to, e.g., 600 to 900° C. so that the second cell 13 b formed of SiO₂ and Ga contained in the second cell 13 b produce a vapor containing Si and Ga (hereinafter, referred to as “Si-containing vapor”). Controlling the beam-equivalent pressure of the Si-containing vapor by changing the heating temperature of the second cell 13 b will control the Si concentration in the Ga₂O₃-based crystal film 1.

Here, the second cell 13 b and Ga contained therein are heated in the contact state and produce the Si-containing vapor. By using the Si-containing vapor produced as such, it is possible to highly accurately control the Si concentration in the Ga₂O₃-based crystal film 1 and also possible to obtain higher uniformity of Si concentration distribution.

When using, e.g., a Si vapor which is produced by using the second cell 13 b formed of SiO₂ and not containing Ga, or a Si vapor which is produced by using a cell formed of PBN, etc., and containing a Si source such as Si, SiO or SiO₂, the Si concentration in the Ga₂O₃-based crystal film 1 cannot be controlled with high accuracy. Also, when using Sn as a dopant, doping delay occurs and Sn may segregate in the Ga₂O₃-based crystal film 1, as mentioned previously.

The present inventors has experimentally confirmed the effect of using the Si-containing vapor produced by the above-described method.

The β-Ga₂O₃-based single crystal constituting the Ga₂O₃-based crystal film 1 is grown at, e.g., a growth temperature of 540° C. and a growth rate of 0.01 to 10 μm/h.

By controlling the Si concentration in the Ga₂O₃-based crystal film 1, the effective donor concentration N_(d)-N_(a) (obtained by subtracting the acceptor concentration N_(a) from the donor concentration N_(d)) is controlled in the range of, e.g., 1×10¹⁵ to 1×10²⁰/cm³.

Second Embodiment

The method of producing the Si-containing vapor in a second embodiment is different from that in the first embodiment. Since the other features are the same as the first embodiment, the explanation thereof will be omitted or simplified.

In the second embodiment, the second cell 13 b may not be formed of SiO₂ and is formed of, e.g., PBN. Then, the second cell 13 b contains Si or a Si compound and Ga. The Si compound is SiO, SiO₂ or a mixture thereof. The form of Si and the Si compound is not specifically limited and is typically a solid such as powder or particles.

Si or Si compound and Ga contained in the second cell 13 b are heated in the contact state and produce the Si-containing vapor. The feature in which the Si-containing vapor is produced by heating a Si source and Ga in the contact state is in common with the first embodiment.

Third Embodiment

The third embodiment is a crystal multilayer structure formed using the methods of growing a Ga₂O₃-based crystal film in the first and second embodiments.

FIG. 3 is a vertical cross sectional view showing a crystal multilayer structure 4 in the third embodiment. The crystal multilayer structure 4 has a Ga₂O₃-based crystal substrate 40, an undoped Ga₂O₃-based crystal film 41 grown on the Ga₂O₃-based crystal substrate 40, a Ga₂O₃-based crystal film 42 containing Si as a dopant and grown directly on the undoped Ga₂O₃-based crystal film 41, and a second undoped Ga₂O₃-based crystal film 43 grown directly on the Ga₂O₃-based crystal film 42.

A laminated structure composed of the undoped Ga₂O₃-based crystal film 41, the Ga₂O₃-based crystal film 42 and the undoped Ga₂O₃-based crystal film 43 is grown by starting and stopping addition of a dopant in the middle of the growth of a Ga₂O₃ crystal on the Ga₂O₃-based crystal substrate 40. The term “undoped” here means that any intentionally added dopant is not contained, and the undoped crystal films do not have a dopant concentration which affects conductivity.

Another Ga₂O₃-based crystal film may be additionally provided between the Ga₂O₃-based crystal substrate 40 and the undoped Ga₂O₃-based crystal film 41.

The Si concentration in the Ga₂O₃-based crystal film 42 is, e.g., not less than 3.0×10¹⁷/cm³ and not more than 3.5×10¹⁹/cm³.

Also, the thickness of the Ga₂O₃-based crystal film 42 is not more than 10 nm. This means that the laminated structure composed of the undoped Ga₂O₃-based crystal film 41, the Ga₂O₃-based crystal film 42 and the undoped Ga₂O₃-based crystal film 43 can be grown only by using the methods of growing a Ga₂O₃-based crystal film in the first and second embodiments in which the Si concentration can be controlled with high accuracy.

Examples of the method of forming a Ga₂O₃-based crystal film other than the MBE method include the PLD (Pulsed Laser Deposition) method, the sputtering method, the MOCVD (Metal Organic Chemical Vapor Deposition) method, the thermal CVD method, the plasma CVD method and the HVPE (Halide Vapor Phase Epitaxy) method, etc., but it is difficult to manufacture the crystal multilayer structure 4 by these methods.

In, e.g., the PLD method and the sputtering method, purity of the film depends on purity of a Ga₂O₃-ceramic target that is a source for forming the film. However, since any high purity Ga₂O₃ target does not currently exist in the world, it is not possible to avoid mixture of unignorable level of impurities and it is thus not possible to form the undoped Ga₂O₃-based crystal films 41 and 43.

Also, in the MOCVD method, the thermal CVD method and the plasma CVD method, impurities from source gases are mixed and, also in this case, it is not possible to form the undoped Ga₂O₃-based crystal films 41 and 43. In the HVPE method, it is possible to form the undoped Ga₂O₃-based crystal films 41 and 43, but it is difficult to form the Ga₂O₃-based crystal film 42 having a thickness of not more than 10 nm since it is not possible to reduce the growth rate.

FIG. 4 is a vertical cross sectional view showing a crystal multilayer structure 5 which is a specific example of the crystal multilayer structure 4. The crystal multilayer structure 5 is suitable for manufacturing, e.g., HEMT (High Electron Mobility Transistor).

The crystal multilayer structure 5 has the Ga₂O₃-based crystal substrate 40, an undoped Ga₂O₃-based crystal film 54 grown on the Ga₂O₃-based crystal substrate 40, an undoped (AlGa)₂O₃ crystal film 51 grown directly on the undoped Ga₂O₃-based crystal film 54, an (AlGa)₂O₃ crystal film 52 grown directly on the undoped (AlGa)₂O₃ crystal film 51, and an undoped (AlGa)₂O₃ crystal film 53 grown directly on the (AlGa)₂O₃ crystal film 52. The (AlGa)₂O₃ crystal film 52 has a thickness of not more than 10 nm and contains Si at a concentration of not less than 3.0×10¹⁷/cm³ and not more than 3.5×10¹⁹/cm³.

The crystal multilayer structure 5 has the undoped (AlGa)₂O₃ crystal film 51, the (AlGa)₂O₃ crystal film 52 and the undoped (AlGa)₂O₃ crystal film 53 which are respectively equivalent to the undoped Ga₂O₃-based crystal film 41, the Ga₂O₃-based crystal film 42 and the undoped Ga₂O₃-based crystal film 43 of the crystal multilayer structure 4. Also, the undoped Ga₂O₃-based crystal film 54 is additionally grown between the Ga₂O₃-based crystal substrate 40 and the undoped (AlGa)₂O₃ crystal film 51.

The undoped (AlGa)₂O₃ crystal film 51, the (AlGa)₂O₃ crystal film 52 and the undoped (AlGa)₂O₃ crystal film 53 are formed of (AlGa)₂O₃ single crystals. The (AlGa)₂O₃ single crystal here means an Al-doped Ga₂O₃ single crystal, i.e., an (Al_(z)Ga_(1-z))₂O₃ single crystal (0≤z<1).

Effects of the Embodiments

In the first and second embodiments, it is possible to provide a method of growing by MBE a Ga₂O₃-based crystal film that allows the highly accurate control of the dopant concentration to enhance the uniformity of dopant concentration distribution. In addition, in the third embodiment, by using the methods of growing a Ga₂O₃-based crystal film in the first and second embodiments, it is possible to provide a crystal multilayer structure including a laminated structure in which a thin Si-doped Ga₂O₃-based crystal film is sandwiched between two undoped Ga₂O₃-based crystal films.

Example 1

The dopant concentration distribution in the thickness direction of the Ga₂O₃-based crystal film grown by using Si or Sn as a dopant was obtained by SIMS analysis.

In this Example, the crystal multilayer structure 4 shown in FIG. 3 was made using Si as a dopant. In detail, the crystal multilayer structure 4 (sample A) was made in which an Sn-doped Ga₂O₃ crystal substrate, a 40 nm-thick undoped Ga₂O₃ crystal film, a 5 nm-thick Ga₂O₃ crystal film containing Si as a dopant and a 40 nm-thick undoped Ga₂O₃ crystal film were respectively provided as the Ga₂O₃-based crystal substrate 40, the undoped Ga₂O₃-based crystal film 41, the Ga₂O₃-based crystal film 42 and the undoped Ga₂O₃-based crystal film 43.

Also, a crystal multilayer structure (sample B) was made as Comparative Example in the same manner as the sample A except that a 5 nm-thick Ga₂O₃ crystal film containing Sn as a dopant was provided instead of the 5 nm-thick Ga₂O₃ crystal film containing Si as a dopant.

The sample A having the Si-doped Ga₂O₃ crystal film was made by the method of growing a Ga₂O₃-based crystal film in the first embodiment. Also, the sample B having the Sn-doped Ga₂O₃ crystal film was made by the method of the first embodiment but a PBN cell containing SnO₂ as a source for producing a Sn vapor was used instead of the second cell 13 b.

FIG. 5A shows Si concentration distribution in a thickness direction in the sample A in which Si is contained as a dopant. FIG. 5B shows Sn concentration distribution in a thickness direction in the sample B in which Sn is contained as a dopant.

In FIGS. 5A and 5B, the horizontal axis indicates a depth from the surface of the Ga₂O₃ crystal film. The arrows of “Open” and “Close” in FIG. 5A respectively indicate the position of the surface of the Ga₂O₃ crystal film at the moment of opening the shutter of the second cell 13 b formed of SiO₂ and the position of the surface of the Ga₂O₃ crystal film at the moment of closing the shutter. Likewise, the arrows of “Open” and “Close” in FIG. 5B respectively indicate the position of the surface of the Ga₂O₃ crystal film at the moment of opening the shutter of the PBN cell containing SnO₂ and the position of the surface of the Ga₂O₃ crystal film at the moment of closing the shutter.

As shown in FIG. 5A, the Si concentration in the Ga₂O₃ crystal film shoots up at the moment of opening the shutter of the second cell 13 b and drops at the moment of closing the shutter. This shows that the laminated structure of the sample A was made as designed.

On the other hand, as shown in FIG. 5B, the Sn concentration in the Ga₂O₃ crystal film gradually increases from the moment of opening the shutter of the cell containing SnO₂ due to doping delay and gradually decreases from the moment of closing the shutter due to segregation on the surface. This shows that the laminated structure of the sample B was not made as designed.

Example 2

An experiment was performed to examine the relation between the heating temperature of the second SiO₂ cell 13 b containing Ga and the effective donor concentration N_(d)-N_(a) in the grown Ga₂O₃-based crystal film 1 in the first embodiment.

In this experiment, a Ga metal was used as Ga to be contained in the second cell 13 b, and a Ga₂O₃ crystal film and a Ga₂O₃ crystal substrate were used as the Ga₂O₃-based crystal film 1 and the Ga₂O₃-based crystal substrate 2.

FIG. 6 shows a relation between an effective donor concentration N_(d)-N_(a) in the Ga₂O₃ crystal film and temperature of the second cell 13 b which is formed of SiO₂ and contains Ga metal.

The effective donor concentration when the temperature of the second cell 13 b is 660° C., 680° C. and 750° C. corresponds to that of the Ga₂O₃ crystal film grown using both the first cell 13 a and the second cell 13 b. Also, the effective donor concentration when the temperature of the second cell 13 b is 900° C. corresponds to that of the Ga₂O₃ crystal film grown using only the second cell 13 b without using the first cell 13 a.

In the method of the first embodiment, the effective donor concentration is the maximum when the Ga₂O₃ crystal film is grown only using the second cell 13 b. Therefore, the effective donor concentration of 3.5×10¹⁹ cm⁻³ obtained when the temperature of the second cell 13 b is 900° C. is considered to be substantially equal to the maximum effective donor concentration of the Ga₂O₃ crystal film. Also, since the effective donor concentration when the temperature of the second cell 13 b is 660° C. is 3.6×10¹⁷ cm⁻³, the minimum controllable effective donor concentration of the Ga₂O₃ crystal film is considered to be about 3.0×10¹⁷/cm³ or less. In the Ga₂O₃ crystal film, the Si concentration is substantially equal to the effective donor concentration.

The result of the experiment shows that, when using the methods of the first and second embodiments, it is possible to control the effective donor concentration of the Ga₂O₃ crystal film at least in the range of not less than 3.0×10¹⁷/cm³ and not more than 3.5×10¹⁹/cm³.

When the second SiO₂ cell 13 b not containing Ga was heated, Si was not introduced into the Ga₂O₃ crystal film even when the temperature was increased to about 1000° C. Probably, this is because enough flux was not generated from the second cell 13 b due to low vapor pressure of SiO₂.

Based on this result, it was confirmed that the important factors to highly accurately control a dopant concentration in a Ga₂O₃-based crystal film are to heat SiO₂ and Ga in the contact state, to produce some chemical reaction between Si, Ga and O, and to produce a Si-containing vapor with an appropriate vapor pressure.

Although the embodiments and Examples of the invention have been described, the invention is not intended to be limited to the embodiments and Examples, and the various kinds of modifications can be implemented without departing from the gist of the invention.

In addition, the invention according to claims is not to be limited to the embodiments and Examples. Further, it should be noted that all combinations of the features described in the embodiments and Examples are not necessary to solve the problem of the invention. 

What is claimed is:
 1. A crystal multilayer structure, comprising: a first undoped β-Ga₂O₃-based crystal film and a second undoped β-Ga₂O₃-based crystal film; and a Si-doped β-Ga₂O₃-based crystal film disposed between the first and second undoped β-Ga₂O₃-based crystal films and having a thickness of not more than 10 nm, wherein the Si-doped β-Ga₂O₃-based crystal film is doped from an interface with the first undoped β-Ga₂O₃-based crystal film to an interface with the second undoped β-Ga₂O₃-based crystal film by controlled concentration of Si.
 2. The crystal multilayer structure according to claim 1, wherein the Si-doped β-Ga₂O₃-based crystal film has an effective donor concentration of 1×10¹⁵/cm³ to 1×10²⁰/cm³.
 3. The crystal multilayer structure according to claim 1, wherein the controlled concentration of Si are from 3.0×10¹⁷/cm³ to 3.5×10¹⁹/cm³ in the Si-doped β-Ga₂O₃-based crystal film.
 4. The crystal multilayer structure according to claim 1, wherein the first undoped β-Ga₂O₃-based crystal film is provided on a β-Ga₂O₃-based crystal substrate.
 5. The crystal multilayer structure according to claim 1, wherein at least one of the first and second undoped β-Ga₂O₃-based crystal films is an undoped β-Ga₂O₃ crystal film.
 6. The crystal multilayer structure according to claim 1, wherein at least one of the first and second undoped β-Ga₂O₃-based crystal films is an undoped β-(AlGa)₂O₃-based crystal film.
 7. A crystal multilayer structure, comprising: a Ga₂O₃-based crystal substrate; an undoped Ga₂O₃-based crystal film grown on the Ga₂O₃-based crystal substrate; a first undoped (AlGa)₂O₃ crystal film grown directly on the undoped Ga₂O₃-based crystal film; a Si-doped (AlGa)₂O₃ crystal film grown directly on the first undoped (AlGa)₂O₃ crystal film, the Si-doped (AlGa)₂O₃ crystal film having a thickness of not more than 10 nm and comprising Si at a concentration of not less than 3.0×10¹⁷/cm³ and not more than 3.5×10¹⁹/cm³; and a second undoped (AlGa)₂O₃ crystal film grown directly on the Si-doped (AlGa)₂O₃ crystal film. 